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<table width="100%" summary="page for Lcomoment.Wk {lmomco}"><tr><td>Lcomoment.Wk {lmomco}</td><td align="right">R Documentation</td></tr></table>
<h2>Weighting Coefficient for Sample L-comoment</h2>


<h3>Description</h3>

<p>
Compute the weight factors for computation of an L-comoment for order <code>k</code>,
order statistic <code>r</code>, and sample size <code>n</code>.
</p>


<h3>Usage</h3>

<pre>
Lcomoment.Wk(k,r,n)
</pre>


<h3>Arguments</h3>

<table summary="R argblock">
<tr valign="top"><td><code>k</code></td>
<td>
Order of L-comoment being computed by parent calls to <code>Lcomoment.Wk</code>.</td></tr>
<tr valign="top"><td><code>r</code></td>
<td>
Order statistic index involved.</td></tr>
<tr valign="top"><td><code>n</code></td>
<td>
Sample size.</td></tr>
</table>

<h3>Details</h3>

<p>
This function computes the weight factors needed to calculation L-comoments
and is interfaced or used by <code>Lcomoment.Lk12</code>. This function is not
necessarily for end users. The weight factor <i>w^{(k)}_{r:n}</i> is the discrete Legendre
polynomial. The weight factors are well illustrated in figure 2.6 of Hosking
and Wallis (1997).
</p>
<p align="center"><i> w^{(k)}_{r:n} = sum_{j=0}^{min{r-1,k-1}} (-1)^{k-1-j}
frac{{k-1 choose j}{k-1+j choose j}
{r-1 choose j}}
{{n-1 choose j}}
mbox{.}</i></p>


<h3>Value</h3>

<p>
A single L-comoment weight factor.</p>

<h3>Note</h3>

<p>
The function begins with a capital letter. This is intentionally done so that lower case 
namespace is preserved. L-comoments are new in the literature and experimental in this package. 
By using a capital letter now, then <code>lcomoment.Wk</code> remains an available name in future 
releases.
</p>


<h3>Author(s)</h3>

<p>
W.H. Asquith
</p>


<h3>Source</h3>

<p>
Serfling and Xiao (2006).
</p>


<h3>References</h3>

<p>
Hosking, J.R.M. and Wallis, J.R., 1997, Regional frequency analysis&mdash;An
approach based on L-moments: Cambridge University Press.
</p>
<p>
Serfling, R., and Xiao, P., 2006, Multivariate L-moments, preprint.
</p>


<h3>See Also</h3>

<p>
<code><a href="Lcomoment.Wk.html">Lcomoment.Wk</a></code>
</p>


<h3>Examples</h3>

<pre>
Wk &lt;- Lcomoment.Wk(2,3,5)
# To compute the weight factors for L-skew and L-coskew (k=3) computation
# for a sample of size 20.
Wk &lt;- matrix(nrow=20,ncol=1)
for(r in seq(1,20)) Wk[r] &lt;- Lcomoment.Wk(3,r,20)
# plot(seq(1,20),Wk)
</pre>



<hr><div align="center">[Package <em>lmomco</em> version 0.92 <a href="00Index.html">Index]</a></div>

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